Homogeneous Map Research Articles

Balanced homogeneous harmonic maps between cones

Balanced homogeneous harmonic maps between cones

Reduced neurovascular coupling of the visual network in migraine patients with aura as revealed with arterial spin labeling MRI: is there a demand-supply mismatch behind the scenes?

BackgroundAlthough neuroimaging investigations have consistently demonstrated that “hyperresponsive” and “hyperconnected” visual cortices may represent the functional substrate of cortical spreading depolarization in patients with migraine with aura, the mechanisms which underpin the brain “tendency” to ignite the cortical spreading depolarization and, consequently, aura phenomenon are still matter of debate. Considering that triggers able to induce aura phenomenon constrain brain to increase global (such as physical activity, stressors and sleep abnormalities) or local (such as bright light visual stimulations) energy demand, a vascular supply unable to satisfy the increased energy requirement could be hypothesized in these patients.MethodsTwenty-three patients with migraine with aura, 25 patients with migraine without aura and 20 healthy controls underwent a 3-Tesla MRI study. Cerebral blood flow and local functional connectivity (regional homogeneity) maps were obtained and registered to the MNI space where 100 cortical regions were derived using a functional local-global normative parcellation. A surrogate estimate of the regional neurovascular coupling for each subject was obtained at each parcel from the correlation coefficient between the z-scored ReHo map and the z-scored cerebral blood flow maps.ResultsA significantly higher regional cerebral blood flow across the visual cortex of both hemispheres (i.e. fusiform and lingual gyri) was detected in migraine with aura patients when compared to patients with migraine without aura (p < 0.05, corrected for multiple comparisons). Concomitantly, a significantly reduced neurovascular coupling (p < 0.05, false discovery rate corrected) in the primary visual cortex parcel (VIS-4) of the large-scale visual network was observed in the left hemisphere of patients with migraine with aura (0.23±0.03), compared to both patients with migraine without aura (0.32±0.05) and healthy controls (0.29±0.05).ConclusionsVisual cortex neurovascular “decoupling” might represent the “link” between the exposure to trigger factors and aura phenomenon ignition. While physiological vascular oversupply may compensate neurovascular demand-supply at rest, it becomes inadequate in case of increased energy demand (e.g. when patients face with trigger factors) paving the way to the aura phenomenon ignition in patients with migraine with aura. Whether preventive treatments may exert their therapeutic activity on migraine with aura restoring the energy demands and cerebral blood flow trade-off within the visual network should be further investigated.

B1 inhomogeneity corrected CEST MRI based on direct saturation removed omega plot model at 5T.

CEST can image macromolecules/compounds via detecting chemical exchange between labile protons and bulk water. B1 field inhomogeneity impairs CEST quantification. Conventional B1 inhomogeneity correction methods depend on interpolation algorithms, B1 choices, acquisition number or calibration curves, making reliable correction challenging. This study proposed a novel B1 inhomogeneity correction method based on a direct saturation (DS) removed omega plot model. Four healthy volunteers underwent B1 field mapping and CEST imaging under four nominal B1 levels of 0.75, 1.0, 1.5, and 2.0 μT at 5T. DS was resolved using a multi-pool Lorentzian model and removed from respective Z spectrum. Residual spectral signals were used to construct the omega plot as a linear function of 1/ , from which corrected signals at nominal B1 levels were calculated. Routine asymmetry analysis was conducted to quantify amide proton transfer (APT) effect. Its distribution across white matter was compared before and after B1 inhomogeneity correction and also with the conventional interpolation approach. B1 inhomogeneity yielded conspicuous artifact on APT images. Such artifact was mitigated by the proposed method. Homogeneous APT maps were shown with SD consistently smaller than that before B1 inhomogeneity correction and the interpolation method. Moreover, B1 inhomogeneity correction from two and four CEST acquisitions yielded similar results, superior over the interpolation method that derived inconsistent APT contrasts among different B1 choices. The proposed method enables reliable B1 inhomogeneity correction from at least two CEST acquisitions, providing an effective way to improve quantitative CEST MRI.

Matrix factorizations and pentagon maps

We propose a specific class of matrices that participate in factorization problems that turn out to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang–Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order N = 2 matrices of this specific class are equivalent to the homogeneous normalization map . From order N = 3 matrices, we obtain an extension of the homogeneous normalization map, as well as novel entwining pentagon, reverse-pentagon and Yang–Baxter maps.

Indoor and outdoor photovoltaic modules Performances based on thin films solar cells

This paper summarizes the electrical and thermal characterizations of thin film PV modules based on amorphous triple junctions (3J: a-Si) and Copper Indium Selenide (CIS) thin film solar cells. Tests are operated in outdoor exposure and under natural sunlight of URAER located in Saharan region of Ghardaïa (Algeria) as specific desert climate environment, characterized by high irradiation and temperature levels as well as ENEA-Portici located in Naples (Italy) as Mediterranean site. PV modules performance evaluation was performed according to international standard as diagnostic test of data manufacturer. We used the thermal infrared analysis to detect the homogeneity mapping temperature of solar cells in the PV module. Data acquired from Environmental Operating Conditions (EOC) was converted into solar module output characteristics at Standard Test Conditions (STC) by using three method suggested by A.J. Anderson and G. Blaesser as well as the equations already standardized as IEC 60891. Then, based on the investigation results of the conversion equations, these methods of translation are distinguished by the type of solar cell technology and the application range. A difference between the tests in situ and in natural environment exists, attributed to various factors but mainly to the mismatch between the spectral responses of PV module and the reference solar cell.

Nonlinear 2-local Lie n-derivations of von Neumann algebras

Let M be a finite von Neumann algebra with no central summands of type I 1. We show that each nonlinear 2-local Lie n-derivation δ : M → M with n ≥ 3 is of the form d + h, where d : M → M is a linear derivation and h is a homogeneous central-valued mapping which annihilates each ( n − 1 ) -th commutator of M .

Decoupling of Regional Cerebral Blood Flow and Brain Function Along the Alzheimer's Disease Continuum.

Alzheimer's disease (AD) is accompanied with impaired neurovascular coupling. However, its early alteration remains elusive along the AD continuum. This study aimed to investigate the early disruption of neurovascular coupling in cognitively normal (CN) and mild cognitive impairment (MCI) elderly and its association with cognition and AD pathologies. We included 43 amyloid-β-negative CN participants and 38 amyloid-β-positive individuals (18 CN and 20 MCI) from the Alzheimer's Disease Neuroimaging Initiative dataset. Regional homogeneity (ReHo) map was used to represent neuronal activity and cerebral blood flow (CBF) map was used to represent cerebral blood perfusion. Neurovascular coupling was assessed by CBF/ReHo ratio at the voxel level. Analyses of covariance to detect the between-group differences and to further investigate the relations between CBF/ReHo ratio and AD biomarkers or cognition. In addition, the correlation of cerebral small vessel disease (SVD) burden and neurovascular coupling was assessed as well. Related to amyloid-β-negative CN group, amyloid-β-positive groups showed decreased CBF/ReHo ratio mainly in the left medial and inferior temporal gyrus. Furthermore, lower CBF/ReHo ratio was associated with a lower Mini-Mental State Examination score as well as higher AD pathological burden. No association between CBF/ReHo ratio and SVD burden was observed. AD pathology is a major correlate of the disturbed neurovascular coupling along the AD continuum, independent of SVD pathology. The CBF/ReHo ratio may be an index for detecting neurovascular coupling abnormalities, which could be used for early diagnosis in the future.

(Best Paper Award) Aluminum Josephson Junction Formation on 200mm Wafers Using Different Oxidation Techniques

For superconducting quantum circuits with a large number of Qubits, reproducible components are crucial for reducing entanglement decoherence. Particularly for reliable industrial manufacturing on full-scale 200 mm' wafers, a very high uniformity level is required to ensure sufficient coherence times. In the present work the special focus was put on manufacturing Al/AlOx/Al Josephson junctions (JJ), which are the most important component of many quantum circuit. Fully Al-based CMOS-compatible JJ’s were produced using a double dry etch process. After patterning the first Al metallization several oxidation processes have been investigated.Static oxidation has been performed by first removing the native AlOx in a multi-chamber system with Ar milling. The final tunneling oxide was controlled by applying a specific pressure in the chamber under a pure O2 atmosphere. Afterwards, without breaking the vacuum, the second Al metallization has been deposited by sputtering. Oxide thicknesses between 1 and 2.5 nm were achieved. A full mapping of the process homogeneity will be given.On the other hand, a dynamic recipe controlled plasma oxidation process was performed, where the native AlOx was first removed by a H2 plasma followed by a defined reoxidation with an oxygen plasma. The resulting oxides had thicknesses up to 10 nm. The second Al metallization was again deposited by sputtering.Both oxidation processes were carefully studied to understand the initial oxidation process of the aluminum surface. Special attention was devoted to the non-destructive removal of the native AlOx with respect to the Al interface. Because the oxide thicknesses varied between 1 and 10 nm, the transition between direct and Fowler-Nordheim tunneling could be investigated. The process-stability on full scale 200 mm wafers and on chip size could be determined via test structures as well as the resistance variation of the Josephson junctions. Furthermore, the electrical properties of the different oxides could be measured and analyzed on wafer level. These studies provide insight into the structure and composition of the aluminum oxides and the applicability for Qubits.

A Cartographic Perspective on the Planetary Geologic Mapping Investigation of Ceres

The NASA Dawn spacecraft visited asteroid 4 Vesta between 2011 and 2012 and dwarf planet 1 Ceres between 2015 and 2018 to investigate their surfaces through optical and hyperspectral imaging and their composition through gamma-ray and neutron spectroscopy. For the global mapping investigation of both proto-planets, geologic mappers employed Geographic Information System (GIS) software to map 15 quadrangles using optical and hyperspectral data and to produce views of the geologic evolution through individual maps and research papers. While geologic mapping was the core motivation of the mapping investigation, the project never aimed to produce homogeneous and consistent map representations. The chosen mapping approach and its implementation led to a number of inconsistencies regarding cartographic representation, including differential generalization through varying mapping scales, topologic inconsistencies, lack of semantic integrity, and scale consistency, and ultimately, to the management of reusable research data. Ongoing data acquisition during the mapping phase created additional challenges for the homogenization of mapping results and a potential derivation of a global map. This contribution reviews cartographic and data perspectives on the mapping investigation of Ceres and highlights (a) data sources, (b) the cartographic concept, (c) mapping conduct, and (d) dissemination as well as research-data management arrangements. It furthermore discusses decisions and experiences made during mapping and finishes with a set of recommendations from the viewpoint of the cartographic sciences.

Penentuan Tingkat Erosi dan Perencanaan Konservasi Lahan di Sub DAS Telagawaja Kabupaten Karangasem Provinsi Bali

&lt;p&gt;The increasing use of natural resources due to population growth and economic development, as well as low public awareness of natural resource conservation, has an impact on accelerating damage to river watersheds. The research aims to determine the level of erosion and its distribution, permitted erosion, conservation planning in the Telagawaja Sub-watershed. The research uses a survey method in taking soil samples based on homogeneous land unit maps. Soil samples were analyzed in the laboratory, erosion calculations used the USLE method. The research results show that the Telagawaja sub-watershed has erosion levels ranging from very light to heavy (0.99-472.19 tons/ha/year). Very light erosion 0.99; 1.53; 5.36 tons/ha/year is found in Homogeneus Land Unit (HLU) I, II, and VII. Heavy erosion 186.64; 221.43; 367.14; 472.19 tons/ha/year is found in HLU V, VI, IV, III. Permissible erosion in the Telagawaja sub-watershed is 11-36.1 tons/ha/year, spread across HLU I is 12.82 tons/ha/year; HLU II of 36.10 tons/ha/year; HLU III of 21.73 tons/ha/year; HLU IV of 24.48 tons/ha/year; HLU V of 13.55 tons/ha/year; HLU VI of 11.00 tons/ha/year; HLU VII is 15.05 tons/ha/year. Conservation actions that can be carried out are by increasing the plant management factor (C) of peanuts with straw mulch of 4 tons/ha (HLU III, IV, V and VI), increasing land management actions by making terracing with medium construction benches (HLU III and IV) and good bench terrace construction (HLU V and VI).&lt;/p&gt;

Finding the Least Element of a Nonnegative Solution Set of a Class of Polynomial Inequalities

In this paper, we consider the least element problem of a nonnegative solution set of a system of inequalities defined by a homogeneous polynomial mapping and a vector. In the set under consideration, the homogeneous polynomial mapping is defined by a tensor. When the tensor involved is square, the set under consideration is just the feasible region of the tensor complementarity problem (TCP). We first introduce the concept of the generalized -tensor, which is a natural generalization of the -tensor. Then, under the assumption that the considered set is nonempty and the tensor involved is a generalized -tensor, we propose an iterative method for finding the least element of the considered set. Specifically, by recognizing the position indices of positive components in the least element continuously, we solve a series of lower-dimensional system of tensor equations corresponding to these indices and prove that the least element of the set can be obtained within finite step iterations. When the tensor involved is square, the least element obtained is also a solution of the TCP. Compared with the existing methods for finding the least-element solution of the TCP with a -tensor, our method does not require any additional assumptions and has lower computational cost. Preliminary numerical experiments show that the proposed method is effective.

A classification‐prediction joint framework to accelerate QTMT‐based CU partition of inter‐mode VVC

AbstractAiming at accelerating the inter coding of versatile video coding (VVC), the existing deep‐learning‐based methods utilize a single convolutional neural network (CNN) to directly predict the quadtree plus multi‐type tree (QTMT)‐based partition of the whole coding tree unit (CTU). However, these methods adopt one prediction network for unevenly distributed CTUs and ignore that the different CTUs have different partition prediction difficulties, leading to performance degradation and computation waste. To overcome these limitations, a classification‐prediction joint framework is proposed to accelerate inter coding of VVC in this letter, which combines classification and prediction to process different CTUs through different networks with appropriate capacities. To achieve effective partition prediction of the whole CTU, the QTMT‐based partition is first modeled as the partition homogeneity map (PHM), which is a value map reflecting the partition of each 8× 8 unit. Second, the classification module classifies the CTUs into different classes according to their partition prediction difficulty, and then different prediction sub‐networks with appropriate capacities are utilized to predict the PHM for the corresponding CTU class. Finally, the decision tree (DT) is adopted to determine the optimal split modes based on the predicted PHM. Experimental results show that the approach achieves 44.5% time saving with 1.94% BD‐BR increase, outperforming state‐of‐the‐art approaches.

A Criterion for Mapping Homogeneity

The paper proposes a definition of a homogeneous mapping based on the concept of a group action. This definition can be used to describe generalizations of the concept of "homogeneous function," including positive, absolute, limited homogeneity, lambda-homogeneity, and homogeneous distributions. The main result is as follows: if a group acts on the set of assignments and values of the mapping, and acts commutatively on the set of values, then the mapping is homogeneous with respect to these actions if and only if the homogeneity condition is satisfied for the generating set of this group.&#x0D; In most cases, the assignment sets and value sets of mappings are vector spaces, and the multiplicative group of the main field or its subgroup acts as an acting group. Therefore, it is important to know their generating sets. For example, for the multiplicative group R+ of positive real numbers, these are numerical intervals, possibly with excluded null sets. Thus, it follows that the homogeneity of a function, understood traditionally, is guaranteed by the fulfillment of the homogeneity condition for any numerical interval from R+. This fact was previously only established for differentiable functions using the well-known Euler identity for homogeneous functions.

On the Solvability of a Periodic Problem for a System of Ordinary Differential Equations with the Main Positive Homogeneous Nonlinearity

We study the solvability of a periodic problem for a system of ordinary differential equations in which we separate the main nonlinear part that is positive homogeneous mapping (of order greater than unity), with the rest called a perturbation. It is proved that if the unperturbed system of equations has no nonzero bounded solutions, then the periodic problem is solvable under any perturbation if and only if the degree of the positive homogeneous mapping on the unit sphere is nonzero. The result obtained is of interest from the point of view of the application and development of methods of nonlinear analysis in the theory of differential and integral equations.

GeoDualCNN: Geometry-Supporting Dual Convolutional Neural Network for Noisy Point Clouds.

We propose a geometry-supporting dual convolutional neural network (GeoDualCNN) for both point cloud normal estimation and denoising. GeoDualCNN fuses the geometry domain knowledge that the underlying surface of a noisy point cloud is piecewisely smooth with the fact that a point normal is properly defined only when local surface smoothness is guaranteed. Centered around this insight, we define the homogeneous neighborhood (HoNe) which stays clear of surface discontinuities, and associate each HoNe with a point whose geometry and normal orientation is mostly consistent with that of HoNe. Thus, we not only obtain initial estimates of the point normals by performing PCA on HoNes, but also for the first time optimize these initial point normals by learning the mapping from two proposed geometric descriptors to the ground-truth point normals. GeoDualCNN consists of two parallel branches that remove noise using the first geometric descriptor (a homogeneous height map, which encodes the point-position information), while preserving surface features using the second geometric descriptor (a homogeneous normal map, which encodes the point-normal information). Such geometry-supporting network architectures enable our model to leverage previous geometry expertise and to benefit from training data. Experiments with noisy point clouds show that GeoDualCNN outperforms the state-of-the-art methods in terms of both noise-robustness and feature preservation.

An analysis of the spatial heterogeneity of future climate change impacts in support of cross-sectoral adaptation strategies in Japan

Addressing climate change requires cross-cutting and effective adaptation strategies. We presented a scenario-based, cross-scale, and spatially explicit framework for analyzing multiple future climate change impacts in Japan. The correlation analysis of climatic and multisectoral impact indicators showed that a complex set of factors, including climate and other indicators used in impact assessment models and how they were used in these models, influenced the correlations. Then, we harmonized and mapped the future impacts in Japan by coupling the K-means multivariate clustering analysis with the similarity search approach. Seven indicators of climate change impacts were utilized to identify the homogeneous impact zones (HIZs) at the end of the 21st century. The homogeneous impact maps of Japan were composed of six HIZs and two isolated impact clusters characterized by varying degrees and combinations of climate change impacts. Changing climates and the cooccurrence of various impacts were context-sensitive. The relationships between the impacts and their coefficient strengths determined the cooccurrence direction. The findings of this study aid us in understanding the compound climate risks, enhancing the synergies and cohesions of adaptation measures, and accelerating science-based adaptation strategies.

The renormalization group transformation in the generalized fermionic hierarchical model

We consider a two-dimensional hierarchical lattice in which the vertices of a square represent an elementary cell. In the generalized hierarchical model, the distance between opposite vertices of a square differs from that between adjacent vertices and is a parameter of the new model. The Gaussian part of the Hamiltonian of the 4-component generalized fermionic hierarchical model is invariant under the block-spin renormalization group transformation. The transformation of the renormalization group in the space of coefficients, which specify the Grassmann-valued density of the free measure, is explicitly calculated as a homogeneous mapping of degree four in the two-dimensional projective space.

Addition of amendments to restore a compacted soil under no-tillage system

The addition of organic and inorganic amendments can improve soil structure and reduce soil compaction. In this context, this study aimed to evaluate whether the application of amendments reduces penetration resistance (PR) in the short term and describe the spatial variability of PR in the surface horizon of an Aquic Argiudoll under no-tillage in northeast Argentina. Four treatments, consisting of surface applications of 7.5 Mg ha−1 poultry litter (PL), 3.0 Mg ha−1 gypsum (G), the combination of PL+G, and untreated control (T), were arranged in a complete randomized block design with three replications. Two more treatments were added to the experiment 12 months later, consisting of PL reapplications on half of the surface of the PL+G and PL treatments (PL+G+PL and PL+PL, respectively) in a split-plot design with three replications in 4×20-m plots. PR was determined in the field with an Eijkelkamp penetrologger following a 2-m long transect perpendicular to the sowing direction at 10 different spots separated 0.2 m from each other. The spatial variability was quantified for each treatment using semivariograms. The highest PR was observed in the T treatment (1.96 MPa) and the lowest PR in PL+G+PL (0.21 MPa). All treatments showed a high spatial dependence (94.9 to 99.9%). Treatments with PL reapplication (PL+PL and PL+G+PL) showed profiles with lower PR and more homogeneous kriging maps. PL reapplication on PL treatments showed no effects on PR values. However, PL reapplication on the PL+G treatment led to positive effects in all PR ranges. Thus, the PL+G+PL treatment, which had the highest PR values, showed a decrease in PR from 54.17 to 6.65% with the reapplication 12 months later. The addition of organic and inorganic amendments reduced specific compacted soil areas on the surface horizon of an Aquic Argiudoll under no-tillage.

OHM: GPU Based Occupancy Map Generation

Occupancy grid maps (OGMs) are fundamental to most systems for autonomous robotic navigation. However, CPU-based implementations struggle to keep up with data rates from modern 3D lidar sensors, and provide little capacity for modern extensions which maintain richer voxel representations. This article presents Occupancy Homogenous Mapping (OHM), our open source, GPU-based OGM framework. We show how the algorithms can be mapped to GPU resources, resolving difficulties with contention to obtain a successful implementation. The implementation supports many modern OGM algorithms including Normal Distributions Transform-Occupancy Maps (NDT-OM), Normal Distributions Transform-Traversability Maps (NDT-TM), decay-rate and Truncated Sign Distance Function (TSDF). A thorough performance evaluation is presented based on tracked and quadruped Uncrewed Ground Vehicle (UGV) platforms and UAVs, and data sets from both outdoor and subterranean environments. The results demonstrate excellent performance improvements both offline, and for online processing in embedded platforms. Finally, we describe how OHM was a key enabler for the UGV navigation solution for our entry in the Defense Advanced Research Projects Agency (DARPA) Subterranean Challenge, which placed second at the Final Event.

Maternal sensitivity at the age of 8 months associates with local connectivity of the medial prefrontal cortex in children at 5 years of age.

The quality of mother–child interaction, especially maternal sensitivity in caregiving behavior, plays an important role in a child’s later socioemotional development. Numerous studies have indicated associations between poor mother–child interaction and offspring brain structure and function, but more knowledge on how variation in the characteristics of early caregiving is associated with children’s brain structure and function is needed. We investigated whether maternal sensitivity at 8 or 30 months is associated with functional connectivity in a child’s brain at 5 years of age based on the FinnBrain Birth Cohort Study (17 and 39 mother–child dyads at 8 and 30 months, respectively, with an overlap of 13 dyads). Maternal sensitivity was assessed during a free play interaction using the Emotional Availability Scales at 8 and 30 months of the children’s age. Task-free functional magnetic resonance imaging (fMRI) was acquired at the age of 5 years in 7-min scans while watching the Inscapes movie. Regional homogeneity (ReHo) maps were created from the fMRI data, and multiple regression analysis was performed to assess the relation between maternal sensitivity and ReHo. Maternal sensitivity at the age of 8 months was positively associated with children’s ReHo values within the medial prefrontal cortex. Distal connectivity of this region showed no significant association with maternal sensitivity in a seed-based connectivity analysis. No associations were found between maternal sensitivity during toddlerhood and brain functional connectivity. Together, these results suggest that maternal sensitivity, especially in infancy, may influence offspring brain functional connectivity. However, studies with larger sample sizes are warranted.